OFFSET
1,2
COMMENTS
This sequence is related to the fourth powers (A000583) by n^4 = n*a(n) - Sum_{i=1..n-1} a(i) - (n-1), with n>1.
Also, n*a(n) - Sum_{i=1..n-1} a(i) provides the first column of A162624 and the second column of A162622 (or A162623). - Bruno Berselli, revised Dec 14 2012
LINKS
B. Berselli, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
MATHEMATICA
CoefficientList[Series[(1 + 5 x + x^2 + x^3) / (1 - x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 19 2013 *)
Table[(4 n^3 - 3 n^2 + 5 n - 3)/3, {n, 1, 40}] (* Bruno Berselli, Feb 17 2015 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 9, 31, 75}, 40] (* Harvey P. Dale, Jul 31 2021 *)
PROG
(PARI) a(n)=(4*n^3-3*n^2+5*n-3)/3 \\ Charles R Greathouse IV, Jun 23 2011
(Magma) [(4*n^3-3*n^2+5*n-3)/3: n in [1..39]]; // Bruno Berselli, Aug 24 2011
(Magma) I:=[1, 9, 31, 75]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Aug 19 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, May 06 2010 - Nov 27 2010
EXTENSIONS
Formulae added and revised by Bruno Berselli, Feb 17 2015
STATUS
approved