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A192396 Square array T(n,k) = floor(((k+1)^n-(1+(-1)^k)/2)/2) read by antidiagonals. 2
0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 4, 4, 2, 0, 0, 8, 13, 8, 2, 0, 0, 16, 40, 32, 12, 3, 0, 0, 32, 121, 128, 62, 18, 3, 0, 0, 64, 364, 512, 312, 108, 24, 4, 0, 0, 128, 1093, 2048, 1562, 648, 171, 32, 4, 0, 0, 256, 3280, 8192, 7812, 3888, 1200, 256, 40, 5, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

T(n,k) is the number of compositions of odd natural numbers into n parts <=k.

LINKS

Table of n, a(n) for n=0..65.

Adi Dani, Restricted compositions of natural numbers

EXAMPLE

T(2,4)=12: there are 12 compositions of odd natural numbers into 2 parts <=4

1: (0,1), (1,0);

3: (1,2), (2,1), (0,3), (3,0);

5: (1,4), (4,1), (2,3), (3,2);

7: (3,4), (4,3).

The table starts

    0,       0,      0,      0,       0,     0,...   A000004

    0,       1,      1,      2,       2,     3,...   A004526

    0,       2,      4,      8,      12,    18,...   A007590

    0,       4,     13,     32,      62,   108,...   A036487

    0,       8,     40,    128,     312,   648,...   A191903

    0,      16,    121,    512,    1562,  3888,...   A191902

    .        .      .       .        .      .        .......

A000004,A000079,A003462,A004171,A128531,A081341,...

MAPLE

A192396 := proc(n, k) (k+1)^n-(1+(-1)^k)/2 ; floor(%/2) ; end proc:

seq(seq( A192396(d-k, k), k=0..d), d=0..10) ; # R. J. Mathar, Jun 30 2011

MATHEMATICA

Table[Table[Floor[1/2*((k + 1)^n - (1 + (-1)^k)/2)], {n, 0, 9}, {k, 0, 9}]]

CROSSREFS

Sequence in context: A089975 A034366 A121465 * A094449 A274776 A274777

Adjacent sequences:  A192393 A192394 A192395 * A192397 A192398 A192399

KEYWORD

nonn,tabl,easy

AUTHOR

Adi Dani, Jun 29 2011

STATUS

approved

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Last modified August 18 20:29 EDT 2018. Contains 313840 sequences. (Running on oeis4.)