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
Keywords
Examples
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.
Links
- Index entries for linear recurrences with constant coefficients, signature (1, 0, 3, -3, 0, -3, 3, 0, 1, -1).
Programs
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Mathematica
LinearRecurrence[{1,0,3,-3,0,-3,3,0,1,-1},{8,26,60,196,308,456,880,1166,1508,2380},40]
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).