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 A118350 Pendular triangle, read by rows, where row n is formed from row n-1 by the recurrence: if n > 2k, T(n,k) = T(n,n-k) + T(n-1,k), else T(n,k) = T(n,n-1-k) + 3*T(n-1,k), for n>=k>=0, with T(n,0)=1 and T(n,n)=0^n. 8
 1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 6, 1, 0, 1, 4, 13, 7, 1, 0, 1, 5, 21, 42, 8, 1, 0, 1, 6, 30, 96, 54, 9, 1, 0, 1, 7, 40, 163, 325, 67, 10, 1, 0, 1, 8, 51, 244, 770, 445, 81, 11, 1, 0, 1, 9, 63, 340, 1353, 2688, 583, 96, 12, 1, 0, 1, 10, 76, 452, 2093, 6530, 3842, 740, 112, 13, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS See definition of pendular triangle and pendular sums at A118340. LINKS FORMULA T(2*n+m,n) = [A118351^(m+1)](n), i.e., the m-th lower semi-diagonal forms the self-convolution (m+1)-power of the central terms A118351. EXAMPLE Row 6 equals the pendular sums of row 5, [1, 4,13, 7, 1, 0], where the sums proceed as follows: [1,__,__,__,__,__]: T(6,0) = T(5,0) = 1; [1,__,__,__,__, 1]: T(6,5) = T(6,0) + 3*T(5,5) = 1 + 3*0 = 1; [1, 5,__,__,__, 1]: T(6,1) = T(6,5) + T(5,1) = 1 + 4 = 5; [1, 5,__,__, 8, 1]: T(6,4) = T(6,1) + 3*T(5,4) = 5 + 3*1 = 8; [1, 5,21,__, 8, 1]: T(6,2) = T(6,4) + T(5,2) = 8 + 13 = 21; [1, 5,21,42, 8, 1]: T(6,3) = T(6,2) + 3*T(5,3) = 21 + 3*7 = 42; [1, 5,21,42, 8, 1, 0] finally, append a zero to obtain row 6. Triangle begins: 1; 1, 0; 1, 1, 0; 1, 2, 1, 0; 1, 3, 6, 1, 0; 1, 4, 13, 7, 1, 0; 1, 5, 21, 42, 8, 1, 0; 1, 6, 30, 96, 54, 9, 1, 0; 1, 7, 40, 163, 325, 67, 10, 1, 0; 1, 8, 51, 244, 770, 445, 81, 11, 1, 0; 1, 9, 63, 340, 1353, 2688, 583, 96, 12, 1, 0; 1, 10, 76, 452, 2093, 6530, 3842, 740, 112, 13, 1, 0; 1, 11, 90, 581, 3010, 11760, 23286, 5230, 917, 129, 14, 1, 0; ... Central terms are T(2*n,n) = A118351(n); semi-diagonals form successive self-convolutions of the central terms: T(2*n+1,n) = A118352(n) = [A118351^2](n), T(2*n+2,n) = A118353(n) = [A118351^3](n). PROG (PARI) T(n, k)=if(n2*k, T(n, n-k)+T(n-1, k), T(n, n-1-k)+3*T(n-1, k))))) CROSSREFS Cf. A118351, A118352, A118353, A118354. Sequence in context: A295860 A118345 A292804 * A183135 A294042 A287316 Adjacent sequences:  A118347 A118348 A118349 * A118351 A118352 A118353 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Apr 26 2006 STATUS approved

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Last modified January 21 16:47 EST 2020. Contains 331114 sequences. (Running on oeis4.)