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A318301 Triangle T(n, k) read by rows: T(0, 0) = 1 and T(n, k) = Sum_{i=0..k-1} T(n, i) + Sum_{i=k..n-1} T(n-1, i). 0
1, 1, 1, 2, 3, 5, 10, 18, 33, 61, 122, 234, 450, 867, 1673, 3346, 6570, 12906, 25362, 49857, 98041, 196082, 388818, 771066, 1529226, 3033090, 6016323, 11934605, 23869210, 47542338, 94695858, 188620650, 275712074, 748391058, 1490765793, 2969596981, 5939193962, 11854518714 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The left edge of the triangle appears to be A005321.

LINKS

Table of n, a(n) for n=0..37.

FORMULA

An equivalent recursion: T(0, 0) = T(1, 0) = 1, T(n, 0) = 2*T(n-1, n-1) if n>=2, T(n, k) = 2*T(n, k-1) - T(n-1, k-1) if n>=k>=1.

EXAMPLE

Triangle begins:

     1

     1    1

     2    3     5

    10   18    33    61

   122  234   450   867  1673

  3346 6570 12906 25362 49857 98041

  ...

T(5, 2) = (3346 + 6570) + (450 + 867 + 1673) = 12906;

T(5, 2) = 2 * 6570 - 234 = 12906.

PROG

(Python)

def T(n, k):

    if k == 0:

        if n == 0 or n == 1:

            return 1

        return 2 * T(n-1, n-1)

    return 2 * T(n, k-1) - T(n-1, k-1)

(PARI) T(n, k) = if (k == 0, if (n <= 1, 1, 2 * T(n-1, n-1)), 2 * T(n, k-1) - T(n-1, k-1));

tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print); \\ Michel Marcus, Aug 25 2018

CROSSREFS

Cf. A005321.

Sequence in context: A117222 A199594 A081172 * A030032 A002661 A216959

Adjacent sequences:  A318298 A318299 A318300 * A318302 A318303 A318304

KEYWORD

nonn,tabl

AUTHOR

Nicolas Nagel, Aug 24 2018

STATUS

approved

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Last modified May 19 04:06 EDT 2019. Contains 323377 sequences. (Running on oeis4.)