OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-6,6,4,-4,-1,1).
FORMULA
a(n) = A014632(n)^2. - Sean A. Irvine, Nov 20 2018
From Colin Barker, Nov 20 2018: (Start)
G.f.: (1 + 24*x + 1196*x^2 + 1280*x^3 + 6294*x^4 + 1976*x^5 + 2828*x^6 + 176*x^7 + 49*x^8) / ((1 - x)^5*(1 + x)^4).
a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) - 6*a(n-4) + 6*a(n-5) + 4*a(n-6) - 4*a(n-7) - a(n-8) + a(n-9) for n>8.
a(n) = 36*n^4 + 60*n^3 + 37*n^2 + 10*n + 1 for n even.
a(n) = 36*n^4 - 12*n^3 + n^2 for n odd.
(End)
MATHEMATICA
Select[Table[PolygonalNumber[5, n]^2, {n, 0, 61}], OddQ] (* James C. McMahon, Dec 24 2023 *)
PROG
(PARI) Vec((1 + 24*x + 1196*x^2 + 1280*x^3 + 6294*x^4 + 1976*x^5 + 2828*x^6 + 176*x^7 + 49*x^8) / ((1 - x)^5*(1 + x)^4) + O(x^40)) \\ Colin Barker, Nov 20 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)
STATUS
approved