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A131270 Triangle T(n,k) = 2*A046854(n,k) - 1, read by rows. 3
1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 5, 1, 1, 1, 5, 5, 7, 1, 1, 1, 5, 11, 7, 9, 1, 1, 1, 7, 11, 19, 9, 11, 1, 1, 1, 7, 19, 19, 29, 11, 13, 1, 1, 1, 9, 19, 39, 29, 41, 13, 15, 1, 1, 1, 9, 29, 39, 69, 41, 55, 15, 17, 1, 1, 1, 11, 29, 69, 69, 111, 55, 71, 17, 19, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums = A131269: {1, 2, 3, 6, 11, 20, 35, 60, 101, 168, ...}.

LINKS

G. C. Greubel, Rows n = 0..100 of triangle, flattened

FORMULA

T(n,k) = 2*A046854(n,k) - 1.

Reversed triangle of A131268.

EXAMPLE

First few rows of the triangle:

  1;

  1,  1;

  1,  1,  1;

  1,  3,  1,  1;

  1,  3,  5,  1,  1;

  1,  5,  5,  7,  1,  1;

  1,  5, 11,  7,  9,  1,  1;

  1,  7, 11, 19,  9, 11,  1,  1;

  ...

MATHEMATICA

Table[2*Binomial[Floor[(n+k)/2], k] - 1, {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jul 09 2019 *)

PROG

(PARI) T(n, k) = 2*binomial((n+k)\2, k)-1; \\ G. C. Greubel, Jul 09 2019

(Magma) [[2*Binomial(Floor((n+k)/2), k) -1: k in [0..n]]:n in [0..12]]; // G. C. Greubel, Jul 09 2019

(Sage) [[2*binomial(floor((n+k)/2), k) -1 for k in (0..n)] for n in (0..12)] # G. C. Greubel, Jul 09 2019

CROSSREFS

Cf. A046854, A065941, A000012, A131268, A131269.

Sequence in context: A243200 A016733 A060234 * A109223 A263009 A283983

Adjacent sequences:  A131267 A131268 A131269 * A131271 A131272 A131273

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jun 23 2007

STATUS

approved

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Last modified May 15 23:51 EDT 2022. Contains 353687 sequences. (Running on oeis4.)