A309372 a(n) = n^2 - n^3 + n^4.
0, 1, 12, 63, 208, 525, 1116, 2107, 3648, 5913, 9100, 13431, 19152, 26533, 35868, 47475, 61696, 78897, 99468, 123823, 152400, 185661, 224092, 268203, 318528, 375625, 440076, 512487, 593488, 683733, 783900, 894691, 1016832, 1151073, 1298188, 1458975, 1634256, 1824877, 2031708, 2255643, 2497600
Offset: 0
Examples
a(4) = 4^2 - 4^3 + 4^4 = 16 - 64 + 256 = 208.
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Crossrefs
Cf. A132998.
Programs
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PARI
concat(0, Vec(x*(1 + 3*x)*(1 + 4*x + x^2) / (1 - x)^5 + O(x^40))) \\ Colin Barker, Aug 11 2019
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Python
for x in range(100): print((x**2)-(x**3)+(x**4))
Formula
From Colin Barker, Aug 11 2019: (Start)
G.f.: x*(1 + 3*x)*(1 + 4*x + x^2) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)