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URL: https://oeis.org/A277792

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A277792
Squares that are also pentagonal pyramidal numbers.
2
0, 1, 196, 2601, 15376, 60025, 181476, 461041, 1032256, 2099601, 3960100, 7027801, 11861136, 19193161, 29964676, 45360225, 66846976, 96216481, 135629316, 187662601, 255360400, 342287001, 452583076, 591024721, 763085376, 975000625, 1233835876, 1547556921, 1925103376, 2376465001, 2912760900
OFFSET
0,3
COMMENTS
Intersection of A000290 and A002411.
FORMULA
O.g.f.: x*(1 + 189*x + 1250*x^2 + 1250*x^3 + 189*x^4 + x^5)/(1 - x)^7.
E.g.f.: x*(1 + 97*x + 336*x^2 + 256*x^3 + 60*x^4 + 4*x^5)*exp(x).
a(n) = a(-n).
a(n) = n^2*(2*n^2 - 1)^2.
a(n) = A000290(A007588(n)).
a(n) = A000290(n)*A000290(A056220(n)).
Sum_{n>=1} 1/a(n) = (2*Pi^2+9*sqrt(2)*Pi*cot(Pi/sqrt(2))+3*Pi^2*csc(Pi/sqrt(2))^2-24)/12 = 1.0055779712856...
EXAMPLE
a(2) = 196 because 196 = 14^2 is a perfect square and 196 = 7^2*(7 + 1)/2 is the 7th pentagonal pyramidal number.
MATHEMATICA
Table[n^2 (2 n^2 - 1)^2, {n, 0, 30}]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 1, 196, 2601, 15376, 60025, 181476}, 40] (* Harvey P. Dale, Nov 01 2024 *)
PROG
(Magma) [n^2*(2*n^2-1)^2: n in [0..30]]; // Vincenzo Librandi, Nov 01 2016
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Oct 31 2016
STATUS
approved