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 A199478 Irregular triangle read by rows: T(n,i) = 2^(i-1)*(binomial(n-i+1,i)+binomial(n-i,i)), n >= 1, 0 <= i <= (n+1)/2. 1
 1, 1, 1, 3, 1, 5, 2, 1, 7, 8, 1, 9, 18, 4, 1, 11, 32, 20, 1, 13, 50, 56, 8, 1, 15, 72, 120, 48, 1, 17, 98, 220, 160, 16, 1, 19, 128, 364, 400, 112, 1, 21, 162, 560, 840, 432, 32, 1, 23, 200, 816, 1568, 1232, 256, 1, 25, 242, 1140, 2688, 2912, 1120, 64, 1, 27 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Row sums are 2^n. T(n,k) is the number of n-letter words from alphabet {a,b,c} not starting with a, having no consecutive letters and exactly k b's. - David Scambler, Dec 10 2011 LINKS G. C. Greubel, Rows n=1..100 of triangle, flattened Eddie Cheng, Ke Qiu and Zhizhang Shen, On the surface area of the augmented cubes, J. of Supercomputing, DOI: 10.1007/s11227-011-0641-1 EXAMPLE Irregular triangle begins : 1, 1 1, 3 1, 5, 2 1, 7, 8 1, 9, 18, 4 1, 11, 32, 20 1, 13, 50, 56, 8 1, 15, 72, 120, 48 1, 17, 98, 220, 160, 16 1, 19, 128, 364, 400, 112 For n=2 one word has no b: ca, and three words have one b: ba, bc, cb. MAPLE scan3:=proc(a, M1) local lis, n, k; lis:=[]; for n from 1 to M1 do for k from 0 to floor((n+1)/2) do lis:=[op(lis), a(n, k)]; od: od: lis; end: a:=(n, i)-> if i=0 then 1 else 2^(i-1)*(binomial(n-i+1, i)+binomial(n-i, i)); fi; scan3(a, 15); MATHEMATICA T[ n_, k_] := Sum[ Binomial[ n - k, i - k] Binomial[ n - i + 1, 2 k - i], {i, 0, n}]; (* Michael Somos, Sep 20 2014 *) PROG (PARI) {T(n, k) = sum(i=0, n, binomial( n-k, i-k) * binomial( n-i+1, 2*k-i))}; /* Michael Somos, Sep 20 2014 */ CROSSREFS Sequence in context: A130303 A100898 A101350 * A134867 A102573 A233940 Adjacent sequences: A199475 A199476 A199477 * A199479 A199480 A199481 KEYWORD nonn,tabf AUTHOR N. J. A. Sloane, Nov 06 2011 STATUS approved

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Last modified January 28 09:01 EST 2023. Contains 359851 sequences. (Running on oeis4.)