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A096977
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a(n) = 4*a(n-1)+3*a(n-2)-14*a(n-3)+8*a(n-4).
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3
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0, 1, 2, 11, 36, 157, 598, 2447, 9672, 38913, 155194, 621683, 2484908, 9943269, 39765790, 159077719, 636281744, 2545185225, 10180624386, 40722730555, 162890456180, 651562756781, 2606249162982, 10425000380191, 41699994064216
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Original name was: A Jacobsthal summation.
The convolution of A024000 and A003683. Inverse binomial transform is A055275, with interpolated zeros.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (4,3,-14,8).
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FORMULA
| G.f.: x*(1-2*x)/((1-x)^2*(1+2*x)*(1-4*x))
a(n) = 4*4^n/27-4*(-2)^n/27+n/9.
a(n) = sum(k=0..n, (A001045(k))^2 ).
a(n) = 4*a(n-1)+3*a(n-2)-14*a(n-3)+8*a(n-4).
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PROG
| (MAGMA) [4*4^n/27-4*(-2)^n/27+n/9: n in [0..30]]; // Vincenzo Librandi, Jul 01 2011
(PARI) a(n)=(4*4^n-4*(-2)^n+3*n)/27 \\ Charles R Greathouse IV, Jul 01 2011
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CROSSREFS
| Cf. A001654.
Sequence in context: A005583 A176916 A015519 * A084098 A152819 A178138
Adjacent sequences: A096974 A096975 A096976 * A096978 A096979 A096980
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 17 2004
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