A054469 A second-order recursive sequence.

1, 7, 28, 85, 218, 499, 1053, 2092, 3970, 7272, 12958, 22596, 38739, 65535, 109714, 182185, 300620, 493635, 807555, 1317360, 2144396, 3485032, 5657028, 9174560, 14869613, 24088399, 39009168, 63156437, 102233030, 165466347, 267786673

Offset

0,2

References

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

A. F. Horadam, Special Properties of the Sequence W(n){a,b; p,q}, Fib. Quart., Vol. 5, No. 5 (1967), pp. 424-434.

A. K. Whitford, Binet's Formula Generalized, Fibonacci Quarterly, Vol. 15, No. 1, 1979, pp. 21, 24, 29.

Index entries for linear recurrences with constant coefficients, signature (6,-14,15,-5,-4,4,-1).

Formula

a(n) = a(n-1)+a(n-2)+(n+2)*C(n+3, 3)/2;

a(n) = a(n-1)+a(n-2)+(n+1)(n+2)^2(n+3)/12;

a(-n) = 0.

a(n) = sum{C(n+5-i, n+2-2i); i=1 to [(n+2)/2]}+2*sum{C(n+5-i, n+1-2i); i=1 to [(n+1)/2]; where [x]=greatest integer in x.

G.f.: (x+1) / ((x-1)^5*(x^2+x-1)). - Colin Barker, Jun 11 2013

Mathematica

RecurrenceTable[{a[0]==1, a[1]==7, a[n]==a[n-1]+a[n-2]+(n+2) Binomial[ n+3, 3]/2}, a, {n, 30}] (* Harvey P. Dale, Sep 22 2013 *)
CoefficientList[Series[(x + 1)/((x - 1)^5 (x^2 + x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 23 2013 *)

Crossrefs

Cf. A001891, A001911.

Right-hand column 11 of triangle A011794.

Sequence in context: A369807 A221141 A144900 * A369806 A156928 A117473

Adjacent sequences: A054466 A054467 A054468 * A054470 A054471 A054472

Keyword

easy,nonn

Author

Barry E. Williams, Mar 31 2000

Status

approved