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)*binomial(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_{i=1..floor((n+2)/2)} binomial(n+5-i, n+2-2*i)) + 2*(Sum_{i=1..floor((n+1)/2)} binomial(n+5-i, n+1-2*i)).
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 *)
PROG
(PARI) a(n) = sum(i=1, (n+2)\2, binomial(n+5-i, n+2-2*i))+2*sum(i=1, (n+1)\2, binomial(n+5-i, n+1-2*i)) \\ Jason Yuen, Aug 13 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Mar 31 2000
STATUS
approved