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A054469 A second-order recursive sequence. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A145135 A221141 A144900 * A156928 A117473 A163037

Adjacent sequences:  A054466 A054467 A054468 * A054470 A054471 A054472

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Mar 31 2000

STATUS

approved

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Last modified June 22 14:27 EDT 2021. Contains 345380 sequences. (Running on oeis4.)