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A132752 Triangle T(n, k) = 2*A132749(n, k) - 1, read by rows. 2
1, 3, 1, 3, 3, 1, 3, 5, 5, 1, 3, 7, 11, 7, 1, 3, 9, 19, 19, 9, 1, 3, 11, 29, 39, 29, 11, 1, 3, 13, 41, 69, 69, 41, 13, 1, 3, 15, 55, 111, 139, 111, 55, 15, 1, 3, 17, 71, 167, 251, 251, 167, 71, 17, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

T(n, k) = 2*A132749(n, k) - 1, an infinite lower triangular matrix.

From G. C. Greubel, Feb 16 2021: (Start)

T(n, k) = A109128(n, k) with T(n, 0) = 3.

Sum_{k=0..n} T(n, k) = 2^(n+1) -n +1 -2*[n=0] = A132753(n) - 2*[n=0]. (End)

EXAMPLE

First few rows of the triangle are:

  1;

  3,  1;

  3,  3,  1;

  3,  5,  5,  1;

  3,  7, 11,  7,  1;

  3,  9, 19, 19,  9,  1;

  3, 11, 29, 39, 29, 11, 1;

  ...

MATHEMATICA

T[n_, k_]:= If[k==n, 1, If[k==0, 3, 2*Binomial[n, k] -1 ]];

Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Feb 16 2021 *)

PROG

(Sage)

def A132752(n, k): return 1 if k==n else 3 if k==0 else 2*binomial(n, k) -1

flatten([[A132752(n, k) for k in [0..n]] for n in [0..12]]) # G. C. Greubel, Feb 16 2021

(Magma)

A132752:= func< n, k | k eq n select 1 else k eq 0 select 3 else 2*Binomial(n, k) -1 >;

[A132752(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 16 2021

CROSSREFS

Cf. A109128, A132749, A132753.

Sequence in context: A234308 A050141 A274773 * A131241 A133599 A256399

Adjacent sequences:  A132749 A132750 A132751 * A132753 A132754 A132755

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Aug 28 2007

STATUS

approved

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Last modified October 23 13:32 EDT 2021. Contains 348214 sequences. (Running on oeis4.)