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A258808
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a(n) = n^7 - 1.
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2
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0, 127, 2186, 16383, 78124, 279935, 823542, 2097151, 4782968, 9999999, 19487170, 35831807, 62748516, 105413503, 170859374, 268435455, 410338672, 612220031, 893871738, 1279999999, 1801088540, 2494357887, 3404825446, 4586471423, 6103515624, 8031810175
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: x^2*(127 + 1170*x + 2451*x^2 + 1156*x^3 + 141*x^4 - 6*x^5 + x^6)/(1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).
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MATHEMATICA
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Table[n^7 - 1, {n, 1, 40}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 127, 2186, 16383, 78124, 279935, 823542, 2097151}, 40]
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PROG
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(Magma) [n^7-1: n in [1..40]] /* or */ I:=[0, 127, 2186, 16383, 78124, 279935, 823542, 2097151]; [n le 8 select I[n] else 8*Self(n-1) - 28*Self(n-2)+56*Self(n-3)-70*Self(n-4)+56*Self(n-5) - 28*Self(n-6) +8*Self(n-7)-Self(n-8): n in [1..40]];
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CROSSREFS
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Cf. similar sequences listed in A258807.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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