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A053296 Partial sums of A053295. 9
1, 8, 37, 129, 376, 967, 2267, 4950, 10220, 20175, 38403, 70954, 127921, 226007, 392688, 672959, 1140260, 1914166, 3189022, 5280288, 8699540, 14275838, 23352118, 38102976, 62048869, 100888126, 163843187, 265838881, 431026972, 698489013, 1131463777, 1832277574, 2966502032, 4802042229 (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. 189, 194-196.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-27,49,-49,21,7,-13,6,-1).

FORMULA

a(n) = Sum_{i=0..floor(n/2)} C(n+7-i, n-2i), n >= 0.

a(n) = a(n-1) + a(n-2) + C(n+6,6); n >= 0; a(-1)=0.

a(n) = Sum_{k=1..n} C(n-k+7,k+6), with n>=0. - Paolo P. Lava, Apr 16 2008

MATHEMATICA

Table[Sum[Binomial[n+7-j, n-2*j], {j, 0, Floor[n/2]}], {n, 0, 50}] (* G. C. Greubel, May 24 2018 *)

PROG

(PARI) for(n=0, 30, print1(sum(j=0, floor(n/2), binomial(n+7-j, n-2*j)), ", ")) \\ G. C. Greubel, May 24 2018

(Magma) [(&+[Binomial(n+7-j, n-2*j): j in [0..Floor(n/2)]]): n in [0..30]]; // G. C. Greubel, May 24 2018

CROSSREFS

Cf. A053739, A014166 and A136431.

Right-hand column 14 of triangle A011794.

Cf. A228074.

Sequence in context: A001780 A258476 A320754 * A055799 A035038 A240188

Adjacent sequences: A053293 A053294 A053295 * A053297 A053298 A053299

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Mar 04 2000

EXTENSIONS

Terms a(28) onward added by G. C. Greubel, May 24 2018

STATUS

approved

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Last modified December 4 07:01 EST 2022. Contains 358544 sequences. (Running on oeis4.)