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 A201509 From abs(A028297)=A034839*A007318 to A165241 via A113402. Second row (double triangle). 4
 1, 1, 2, 2, 4, 5, 1, 8, 12, 4, 16, 28, 13, 1, 32, 64, 38, 6, 64, 144, 104, 25, 1, 128, 320, 272, 88, 8, 256, 704, 688, 280, 41, 1, 512, 1536, 1696, 832, 170, 10, 1024, 3328, 4096, 2352, 620, 61, 1, 2048, 7168 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Consider the irregular blocks of k verticals 1  1    2 1    4 3      8  8  1       16 20  5          32  48  18   1    1 1  2 2    4 5 1    8 12  4       16 28 13  1       32  64  38   6         2 3 1  4 7 3    8 16  9  1    16 36 25  5       32  80  66  19   1                4 9 6 1  8 20 16  4    16 44 41 14  1    32  96 102  44   6                         8 24 25 10 1  16 52 61 30  5    32 112 146  85  20  1                                       16 60 85 55 15 1  32 128 198 146  50  6                                                         32 144 258 231 105 21 1. Without spaces the first row is abs(A028297) from Chebyshev polynomials. Note partial sums: 1,1,3,7,17,...=A001333. First verticals are A113402. Vertical sums: 1,2,6,16,40,...=A057711(n+1)=A129952(n+1). Algorithm: 1) The first 1 of row 1 (or first vertical) gives the second 1 of the second row.            2) 1 1 of the second vertical is the difference of the fifth vertical; 1 of third vertical is 1 of the sixth.            3) 2 2 2 of the fourth vertical gives 1 3 5 7 of the eighth; 1 2 3 of the fifth gives 0 (not written) 1 3 6 of the ninth; 1 of the sixth gives 1 of the tenth vertical. A201509 is the pseudo-triangle whose successive lines are of the type T(n,0), T(n,1)+T(n-1,0), T(n,2)+T(n-1,1), ... T(n,k)+T(n-1,k-1), without 0's, with T=A201701. [e-mail, Philippe Deléham, Dec 04 2011] a(n)= 1     1 2     2 4     5   1 8    12   4 16   28  13  1 32   64  38  6 64  144 104 25 1 128 320 272 88 8 Row sums=2,4,10,24=A052542(n+1). Odd terms row sums: 1,2,5,12,29,70,...=A000129(n+1); also for even terms. Terms of last row blocks: A165241. Verticals: see A000079, A045623, A049611, A055585. b(n)= 1,1, 2,2,0, 4,5,1,0, 8,12,4,0,0, 16,28,13,1,0,0, could be considered. LINKS FORMULA T(n,k)= 2*T(n-1,k) + T(n-2,k-1) with T(0,0) = 0, T(n,0) = T(1,1) = 1 and T(n,k) = 0 if k<0 or if n

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Last modified June 25 03:59 EDT 2022. Contains 354835 sequences. (Running on oeis4.)