A218331 Even, nonzero decagonal pyramidal numbers.
38, 90, 476, 708, 1826, 2366, 4600, 5576, 9310, 10850, 16468, 18700, 26586, 29638, 40176, 44176, 57750, 62826, 79820, 86100, 106898, 114510, 139496, 148568, 178126, 188786, 223300, 235676, 275530, 289750, 335328, 351520, 403206, 421498, 479676, 500196
Offset: 1
Examples
The sequence of nonzero decagonal pyramidal numbers begins 1, 11, 38, 90, 175, 301, 476, 708, 1005, 1375,... As the third even term is 476, then a(3) = 476.
Links
- Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
Programs
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Mathematica
LinearRecurrence[{1,3,-3,-3,3,1,-1},{38,90,476,708,1826,2366,4600},36]
Formula
a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7).
a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) + 512.
a(n) = (16*n-4*(-1)^n-1)*(4*n-(-1)^n+3)*(4*n-(-1)^n+1)/24.
G. f. 2*x*(19+26*x+136*x^2+38*x^3+37*x^4)/((1-x)^4*(1+x)^3).