A254654 -id:A254654 - cp's OEIS frontend

A254652 Indices of pentagonal numbers (A000326) which are also centered heptagonal numbers (A069099).

1, 4, 88, 421, 9661, 46288, 1062604, 5091241, 116876761, 559990204, 12855381088, 61593831181, 1413975042901, 6774761439688, 155524399338004, 745162164534481, 17106269952137521, 81961063337353204, 1881534170335789288, 9014971804944317941

Offset: 1

Colin Barker, Feb 04 2015

Also positive integers x in the solutions to 3*x^2 - 7*y^2 - x + 7*y - 2 = 0, the corresponding values of y being A254653.

			4 is in the sequence because the 4th pentagonal number is 22, which is also the 3rd centered heptagonal number.

Colin Barker, Table of n, a(n) for n = 1..980
Index entries for linear recurrences with constant coefficients, signature (1,110,-110,-1,1).

Cf. A000326, A069099, A254653, A254654.

LinearRecurrence[{1,110,-110,-1,1},{1,4,88,421,9661},30] (* Harvey P. Dale, Dec 09 2018 *)

Vec(-x*(x^2-4*x+1)*(x^2+7*x+1)/((x-1)*(x^4-110*x^2+1)) + O(x^100))

a(n) = a(n-1)+110*a(n-2)-110*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^2-4*x+1)*(x^2+7*x+1) / ((x-1)*(x^4-110*x^2+1)).

A254653 Indices of centered heptagonal numbers (A069099) which are also pentagonal numbers (A000326).

Original entry on oeis.org

1, 3, 58, 276, 6325, 30303, 695638, 3333000, 76513801, 366599643, 8415822418, 40322627676, 925663952125, 4435122444663, 101814618911278, 487823146285200, 11198682416288401, 53656110968927283, 1231753251172812778, 5901684383435715876, 135481658946593117125

Offset: 1

Colin Barker, Feb 04 2015

Also positive integers y in the solutions to 3*x^2 - 7*y^2 - x + 7*y - 2 = 0, the corresponding values of x being A254652.

			3 is in the sequence because the 3rd centered heptagonal number is 22, which is also the 4th pentagonal number.

Colin Barker, Table of n, a(n) for n = 1..980
Index entries for linear recurrences with constant coefficients, signature (1,110,-110,-1,1).

Cf. A000326, A069099, A254652, A254654.

Vec(x*(2*x^3+55*x^2-2*x-1)/((x-1)*(x^4-110*x^2+1)) + O(x^100))

a(n) = a(n-1)+110*a(n-2)-110*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(2*x^3+55*x^2-2*x-1) / ((x-1)*(x^4-110*x^2+1)).

cp's OEIS Frontend

A254652 Indices of pentagonal numbers (A000326) which are also centered heptagonal numbers (A069099).

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