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 A176508 Triangle, read by rows, defined by T(n, k) = b(n) - b(k) - b(n-k) + 1, b(n) = A003269(n). 1
 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 3, 3, 2, 1, 1, 1, 1, 2, 3, 4, 3, 2, 1, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 3, 5, 6, 7, 7, 7, 6, 5, 3, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,24 COMMENTS Row sums are: {1, 2, 2, 2, 2, 6, 10, 14, 18, 30, 51,...}. LINKS Indranil Ghosh, Rows 0..100, flattened Indranil Ghosh, Python Program to generate the b-file FORMULA T(n,m) = A003269(n) - A003269(m) - A003269(n-m) + 1. EXAMPLE Triangle:   1;   1, 1;   1, 0, 1;   1, 0, 0, 1;   1, 0, 0, 0, 1;   1, 1, 1, 1, 1, 1;   1, 1, 2, 2, 2, 1, 1;   1, 1, 2, 3, 3, 2, 1, 1;   1, 1, 2, 3, 4, 3, 2, 1, 1;   1, 2, 3, 4, 5, 5, 4, 3, 2, 1;   1, 3, 5, 6, 7, 7, 7, 6, 5, 3, 1; ... T(6,3) = A003269(6) - A003269(3) - A003269(6-3) + 1 = 3 - 1 - 1 + 1 = 2. - Indranil Ghosh, Feb 17 2017 MATHEMATICA b[0]:= 0; b[1]:= 1; b[2]:= 1; b[3]:= 1; b[n_]:= b[n] = b[n-1] + b[n-4]; T[n_, m_]:= b[n] - b[m] - b[n-m] + 1; Table[T[n, m], {n, 0, 10}, {m, 0, n} ]//Flatten PROG (Python) # See Indranil Ghosh link (PARI) {b(n) = if(n==0, 0, if(n==1, 1, if(n==2, 1, if(n==3, 1, b(n-1) +b(n-4)))) )}; {T(n, k) = b(n) -b(k) -b(n-k) +1}; \\ G. C. Greubel, May 06 2019 (MAGMA) b:= func< n | n eq 0 select 0 else (&+[Binomial(n-1-3*j, j): j in [0..Floor((n-1)/3)]]) >; [[b(n)-b(k)-b(n-k)+1: k in [0..n]]: n in [0..10]]; // G. C. Greubel, May 06 2019 (Sage) def b(n):     if (n==0): return 0     elif (n==1): return 1     elif (n==2): return 1     elif (n==3): return 1     else: return b(n-1) + b(n-4) def T(n, k): return b(n) - b(k) - b(n-k) + 1 [[T(n, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, May 06 2019 CROSSREFS Cf. A003269. Sequence in context: A037804 A316894 A081503 * A241492 A227739 A047971 Adjacent sequences:  A176505 A176506 A176507 * A176509 A176510 A176511 KEYWORD nonn,easy,tabl AUTHOR Roger L. Bagula, Apr 19 2010 EXTENSIONS Name and formula sections were edited and corrected by Indranil Ghosh, Feb 17 2017 Edited by G. C. Greubel, May 06 2019 STATUS approved

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Last modified December 1 11:01 EST 2021. Contains 349429 sequences. (Running on oeis4.)