OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).
FORMULA
Binomial transform of (1, 5, 5, 1, 1, 1, ...).
G.f.: 1-2*x*(-3+7*x-3*x^2+x^3) / ( (2*x-1)*(x-1)^3 ). - R. J. Mathar, Apr 04 2012
From Colin Barker, Nov 04 2017: (Start)
a(n) = 2^n + 2*n + 2*n^2.
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n > 3.
(End)
EXAMPLE
a(3) = 32 = sum of row 3 terms, triangle A131948: (7 + 9 + 9 + 7).
a(3) = 32 = (1, 3, 3, 1) dot (1, 5, 5, 1) = (1 + 15 + 15 + 1).
MATHEMATICA
LinearRecurrence[{5, -9, 7, -2}, {1, 6, 16, 32}, 30] (* Harvey P. Dale, Feb 24 2016 *)
PROG
(PARI) Vec((1 + x - 5*x^2 - x^3) / ((1 - x)^3*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Nov 04 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jul 30 2007
STATUS
approved