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A014769 Squares of odd pentagonal numbers. 1
1, 25, 1225, 2601, 13689, 21025, 61009, 82369, 180625, 227529, 423801, 511225, 855625, 1002001, 1555009, 1782225, 2614689, 2948089, 4141225, 4609609, 6255001, 6890625, 9090225, 9928801, 12794929, 13875625, 17530969, 18896409, 23474025, 25170289, 30813601 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Cf. A014632.
Odd terms of A100255.
Sequence in context: A012799 A120694 A012809 * A012851 A181719 A096330
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)
STATUS
approved

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Last modified July 15 07:59 EDT 2024. Contains 374324 sequences. (Running on oeis4.)