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A118416 Triangle read by rows: T(n,k) = (2*k-1)*2^(n-1), 0<k<=n. 15
1, 2, 6, 4, 12, 20, 8, 24, 40, 56, 16, 48, 80, 112, 144, 32, 96, 160, 224, 288, 352, 64, 192, 320, 448, 576, 704, 832, 128, 384, 640, 896, 1152, 1408, 1664, 1920, 256, 768, 1280, 1792, 2304, 2816, 3328, 3840, 4352, 512, 1536, 2560, 3584, 4608, 5632, 6656, 7680 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums give A014477: sum(k=1..n, T(n,k) ) = A014477(n-1);

central terms give A118415; T(2*k-1,k) = A058962(k-1);

T(n,1) = A000079(n-1);

T(n,2) = A007283(n-1) for n>1;

T(n,3) = A020714(n-1) for n>2;

T(n,4) = A005009(n-1) for n>3;

T(n,5) = A005010(n-1) for n>4;

T(n,n-1) = A118417(n-1) for n>1;

T(n,n) = A014480(n-1) = A118413(n,n);

A001511(T(n,k)) = A002024(n,k);

A003602(T(n,k)) = A002260(n,k).

LINKS

Reinhard Zumkeller, Rows n=1..100 of triangle, flattened

FORMULA

T(n,k) = 2*T(n-1,k), 1 <= k < n; T(n,n) = A014480(n-1).

EXAMPLE

1;

2, 6;

4, 12, 20;

8, 24, 40, 56;

16, 48, 80, 112, 144;

32, 96, 160, 224, 288, 352;

64, 192, 320, 448, 576, 704, 832;

MAPLE

A118416 := proc(n, k) 2^(n-1)*(2*k-1) ; end proc: # R. J. Mathar, Sep 04 2011

MATHEMATICA

Flatten[Table[(2k-1)2^(n-1), {n, 10}, {k, n}]] (* Harvey P. Dale, Aug 26 2014 *)

PROG

(Haskell)

a118416 n k = a118416_tabl !! (n-1) !! (k-1)

a118416_row 1 = [1]

a118416_row n = (map (* 2) $ a118416_row (n-1)) ++ [a014480 (n-1)]

a118416_tabl = map a118416_row [1..]

-- Reinhard Zumkeller, Jan 22 2012

CROSSREFS

Cf. A118413, A117303, A054582.

Sequence in context: A072946 A134000 A127730 * A046204 A163755 A100851

Adjacent sequences:  A118413 A118414 A118415 * A118417 A118418 A118419

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Apr 27 2006

STATUS

approved

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Last modified October 17 21:41 EDT 2018. Contains 316293 sequences. (Running on oeis4.)