A118413 - OEIS

A118413

Triangle read by rows: T(n,k) = (2*n-1)*2^(k-1), 0<k<=n.

1, 3, 6, 5, 10, 20, 7, 14, 28, 56, 9, 18, 36, 72, 144, 11, 22, 44, 88, 176, 352, 13, 26, 52, 104, 208, 416, 832, 15, 30, 60, 120, 240, 480, 960, 1920, 17, 34, 68, 136, 272, 544, 1088, 2176, 4352, 19, 38, 76, 152, 304, 608, 1216, 2432, 4864, 9728, 21, 42, 84, 168

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OFFSET

1,2

COMMENTS

Central terms give A118415; row sums give A118414;

T(n,1) = A005408(n-1);

T(n,2) = A016825(n-1) for n>1;

T(n,3) = A017113(n-1) for n>2;

T(n,4) = A051062(n-1) for n>3;

T(n,n-2) = A052951(n-1) for n>2;

T(n,n) = A014480(n-1) = A118416(n,n);

A001511(T(n,k)) = A002260(n,k);

A003602(T(n,k)) = A002024(n,k).

G.f.: x*y*(1 + x + 2*x*y - 6*x^2*y)/((1 - x)^2*(1 - 2*x*y)^2). - Stefano Spezia, Dec 22 2024

LINKS

Table of n, a(n) for n=1..59.

EXAMPLE

3 6

5 10 20

7 14 28 56

9 18 36 72 144

11 22 44 88 176 352

13 26 52 104 208 416 832

15 30 60 120 240 480 960 1920

17 34 68 136 272 544 1088 2176 4352

19 38 76 152 304 608 1216 2432 4864 9728

...

MATHEMATICA

Select[Flatten[Table[(2n-1)2^(k-1), {n, 20}, {k, 0, n}]], IntegerQ] (* Harvey P. Dale, Jan 17 2024 *)

CROSSREFS

Cf. A001511, A002024, A002260, A003602, A005408, A014480, A016825, A017113, A051062, A052951, A117303, A118414, A118415, A118416, A117303.

Sequence in context: A246978 A127780 A350661 * A295320 A093419 A160049

Adjacent sequences: A118410 A118411 A118412 * A118414 A118415 A118416

KEYWORD

nonn,tabl,easy

AUTHOR

Reinhard Zumkeller, Apr 27 2006

STATUS

approved