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A097333 a(n) = Sum_{k=0..n} C(n-k, floor(k/2)). 19
1, 2, 2, 3, 5, 7, 10, 15, 22, 32, 47, 69, 101, 148, 217, 318, 466, 683, 1001, 1467, 2150, 3151, 4618, 6768, 9919, 14537, 21305, 31224, 45761, 67066, 98290, 144051, 211117, 309407, 453458, 664575, 973982, 1427440, 2092015, 3065997, 4493437, 6585452 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A058278.

LINKS

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

Engin Özkan, Bahar Kuloǧlu, and James Peters, k-Narayana sequence self-similarity, hal-03242990 [math.CO], 2021. See p. 12.

Index entries for linear recurrences with constant coefficients, signature (1,0,1).

FORMULA

G.f. : (1+x-x^2-x^3)/((1-x)*(1-x^2-x^3-x^4)) = (1+x)/(1-x-x^3);

a(n) = a(n-1) + a(n-3);

a(n) = a(n-1) + a(n-2) - a(n-5).

MATHEMATICA

LinearRecurrence[{1, 0, 1}, {1, 2, 2}, 70] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2011*)

PROG

(PARI) a(n) = sum(k=0, n, binomial(n-k, k\2)); \\ Michel Marcus, Mar 02 2022

CROSSREFS

Cf. A003410.

Sequence in context: A320689 A173693 A058278 * A001083 A173696 A120412

Adjacent sequences:  A097330 A097331 A097332 * A097334 A097335 A097336

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Aug 05 2004

STATUS

approved

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Last modified October 6 10:31 EDT 2022. Contains 357263 sequences. (Running on oeis4.)