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 A239662 Triangle read by rows: T(n,k), n>=1, k>=1, in which column k lists the numbers A017113 interleaved with k-1 zeros, and the first element of column k is in row k(k+1)/2. 3
 4, 12, 20, 4, 28, 0, 36, 12, 44, 0, 4, 52, 20, 0, 60, 0, 0, 68, 28, 12, 76, 0, 0, 4, 84, 36, 0, 0, 92, 0, 20, 0, 100, 44, 0, 0, 108, 0, 0, 12, 116, 52, 28, 0, 4, 124, 0, 0, 0, 0, 132, 60, 0, 0, 0, 140, 0, 36, 20, 0, 148, 68, 0, 0, 0, 156, 0, 0, 0, 12, 164, 76, 44, 0, 0, 4, 172, 0, 0, 28, 0, 0, 180, 84, 0, 0, 0, 0, 188, 0, 52, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Gives an identity for A239050. Alternating sum of row n equals A239050(n), i.e., sum_{k=1..A003056(n))} (-1)^(k-1)*T(n,k) = 4*A000203(n) = 2*A074400(n) = A239050(n). Row n has length A003056(n) hence the first element of column k is in row A000217(k). Note that if T(n,k) = 12 then T(n+1,k+1) = 4, the first element of the column k+1. The number of positive terms in row n is A001227(n). For more information see A196020. Column 1 is A017113. - Omar E. Pol, Apr 17 2016 LINKS FORMULA T(n,k) = 2*A236106(n,k) = 4*A196020(n,k). EXAMPLE Triangle begins: 4; 12; 20,   4; 28,   0; 36,  12; 44,   0,  4; 52,  20,  0; 60,   0,  0; 68,  28, 12; 76,   0,  0,  4; 84,  36,  0,  0; 92,   0, 20,  0; 100, 44,  0,  0; 108,  0,  0, 12; 116, 52, 28,  0,  4; 124,  0,  0,  0,  0; 132, 60,  0,  0,  0; 140,  0, 36, 20,  0; 148, 68,  0,  0,  0; 156,  0,  0,  0, 12; 164, 76, 44,  0,  0,  4; 172,  0,  0, 28,  0,  0; 180, 84,  0,  0,  0,  0; 188,  0, 52,  0,  0,  0; ... For n = 9, the 9th row of triangle is [68, 28, 12], therefore the alternating row sum is 68 - 28 + 12 = 52. On the other hand we have that 4*A000203(9) = 2*A074400(9) = A239050(9) = 4*13 = 2*26 = 52, equaling the alternating sum of the 9th row of the triangle. CROSSREFS Cf. A000203, A000217, A003056, A017113, A074400, A196020, A211343, A235791, A236104, A236106, A236112, A237048, A237591, A239050, A239446. Sequence in context: A009557 A240762 A050021 * A321769 A133096 A309085 Adjacent sequences:  A239659 A239660 A239661 * A239663 A239664 A239665 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Mar 30 2014 STATUS approved

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Last modified August 22 20:23 EDT 2019. Contains 326182 sequences. (Running on oeis4.)