A218325 Even heptagonal pyramidal numbers.

8, 26, 60, 196, 308, 456, 880, 1166, 1508, 2380, 2920, 3536, 5016, 5890, 6860, 9108, 10396, 11800, 14976, 16758, 18676, 22940, 25296, 27808, 33320, 36330, 39516, 46436, 50180, 54120, 62608, 67166, 71940, 82156, 87608, 93296, 105400, 111826, 118508, 132660

Offset

1,1

Links

Table of n, a(n) for n=1..40.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 3, -3, 0, -3, 3, 0, 1, -1).

Formula

a(n) = a(n-1) + 3*a(n-3) - 3*a(n-4) - 3*a(n-6) + 3*a(n-7) + a(n-9) - a(n-10).

a(n) = 3*a(n-3) - 3*a(n-6) + a(n-9) + 320.

a(n) = (phi(n)+3)*(phi(n)+12)(5*phi(n)-3)/4374, where phi(n) = 12*n - 3*cos(2*n*pi/3) + sqrt(3)*sin(2*n*pi/3).

G. f. 2*x*(4+9*x+17*x^2+56*x^3+29*x^4+23*x^5+20*x^6+2*x^7) / ((1-x)^4*(1+x+x^2)^3).

Example

The sequence of heptagonal pyramidal numbers A002413(n) begins 1, 8, 26, 60, 115, 196, 308, 456, 645, 880, … As the third even term is 60, then a(3) = 60.

Mathematica

LinearRecurrence[{1, 0, 3, -3, 0, -3, 3, 0, 1, -1}, {8, 26, 60, 196, 308, 456, 880, 1166, 1508, 2380}, 40]

Crossrefs

Cf. A002413, A218324.

Sequence in context: A111694 A129111 A002413 * A363288 A252870 A163121

Adjacent sequences: A218322 A218323 A218324 * A218326 A218327 A218328

Keyword

nonn

Author

Ant King, Oct 26 2012

Status

approved