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A152842 Triangle T(n,k), 0 <= k <= n, read by rows, given by [1,0,-1,0,0,0,0,0,0,...] DELTA [3,-2,-1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. 5
1, 1, 3, 1, 4, 3, 1, 7, 15, 9, 1, 8, 22, 24, 9, 1, 11, 46, 90, 81, 27, 1, 12, 57, 136, 171, 108, 27, 1, 15, 93, 307, 579, 621, 351, 81, 1, 16, 108, 400, 886, 1200, 972, 432, 81, 1, 19, 156, 724, 2086, 3858, 4572, 3348, 1377, 243, 1, 20, 175, 880, 2810, 5944, 8430, 7920 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Reinhard Zumkeller, Rows n = 0..125 of table, flattened

FORMULA

T(n,k) = T(n-1,k) + (2-(-1)^n)*(T(n-1,k-1).

Sum_{k=0..n} T(n,k) = A094015(n).

T(n,n) = A108411(n+1).

T(2n,n) = A069835(n).

G.f.: (1+x+x*y)/(1-x^2-4*x^2*y-3*x^2*y^2). - Philippe Deléham , Nov 09 2013

T(n,k) = T(n-2,k) + 4*T(n-2,k-1) + 3*T(n-2,k-2), T(0,0) = T(1,0) = 1, T(1,1) = 3, T(n,k) = 0 if k < 0 or if k > n. - Philippe Deléham, Nov 09 2013

EXAMPLE

The triangle T(n,k) begins:

n\k  0   1    2     3     4      5      6      7      8      9     10    11   12

0:   1

1:   1   3

2:   1   4    3

3:   1   7   15     9

4:   1   8   22    24     9

5:   1  11   46    90    81     27

6:   1  12   57   136   171    108     27

7:   1  15   93   307   579    621    351     81

8:   1  16  108   400   886   1200    972    432     81

9:   1  19  156   724  2086   3858   4572   3348   1377    243

10:  1  20  175   880  2810   5944   8430   7920   4725   1620    243

11:  1  23  235  1405  5450  14374  26262  33210  28485  15795   5103   729

12:  1  24  258  1640  6855  19824  40636  59472  61695  44280  20898  5832  729

... reformatted and extended. - Franck Maminirina Ramaharo, Feb 28 2018

PROG

(Haskell)

a152842 n k = a152842_tabl !! n !! k

a152842_row n = a152842_tabl !! n

a152842_tabl = map fst $ iterate f ([1], 3) where

   f (xs, z) = (zipWith (+) ([0] ++ map (* z) xs) (xs ++ [0]), 4 - z)

-- Reinhard Zumkeller, May 01 2014

CROSSREFS

Cf. A152815, A007318, A064861.

Sequence in context: A322103 A272172 A104764 * A307280 A209704 A082909

Adjacent sequences:  A152839 A152840 A152841 * A152843 A152844 A152845

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Dec 14 2008

STATUS

approved

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Last modified July 4 11:58 EDT 2020. Contains 335448 sequences. (Running on oeis4.)