The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A093190 Array t read by antidiagonals: number of {112,212}-avoiding words. 1
 1, 1, 2, 1, 4, 3, 1, 6, 9, 4, 1, 8, 21, 16, 5, 1, 10, 39, 52, 25, 6, 1, 12, 63, 136, 105, 36, 7, 1, 14, 93, 292, 365, 186, 49, 8, 1, 16, 129, 544, 1045, 816, 301, 64, 9, 1, 18, 171, 916, 2505, 3006, 1603, 456, 81, 10, 1, 20, 219, 1432, 5225, 9276, 7315, 2864, 657, 100, 11 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS t(k,n) = number of n-long k-ary words that simultaneously avoid the patterns 112 and 212. LINKS G. C. Greubel, Antidiagonal rows n = 1..50, flattened A. Burstein and T. Mansour, Words restricted by patterns with at most 2 distinct letters, arXiv:math/0110056 [math.CO], 2001. FORMULA t(n, k) = Sum{j=0..n} j!*C(n, j)*C(k-1, j-1). (square array) T(n, k) = Sum_{j=0..n-k+1} j!*binomial(k,j)*binomial(n-k,j-1). (number triangle) - G. C. Greubel, Mar 09 2021 EXAMPLE Square array begins as: 1 1 1 1 1 1 ... 1*A000012; 2 4 6 8 10 12 ... 2*A000027; 3 9 21 39 63 93 ... 3*A002061; 4 16 52 136 292 544 ... 4*A135859; 5 25 105 365 1045 2505 ... ; Antidiagonal rows begins as: 1; 1, 2; 1, 4, 3; 1, 6, 9, 4; 1, 8, 21, 16, 5; 1, 10, 39, 52, 25, 6; 1, 12, 63, 136, 105, 36, 7; MATHEMATICA T[n_, k_]:= Sum[j!*Binomial[k, j]*Binomial[n-k, j-1], {j, 0, n-k+1}]; Table[T[n, k], {n, 12}, {k, n}]//Flatten (* G. C. Greubel, Mar 09 2021 *) PROG (PARI) t(n, k)=sum(j=0, k, j!*binomial(k, j)*binomial(n-1, j-1)) (Sage) flatten([[ sum(factorial(j)*binomial(k, j)*binomial(n-k, j-1) for j in (0..n-k+1)) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Mar 09 2021 (Magma) [(&+[Factorial(j)*Binomial(k, j)*Binomial(n-k, j-1): j in [0..n-k+1]]): k in [1..n], n in [1..12]]; // G. C. Greubel, Mar 09 2021 CROSSREFS Main diagonal is A052852. Antidiagonal sums are in A084261 - 1. Sequence in context: A103406 A142978 A152060 * A132191 A094437 A172431 Adjacent sequences: A093187 A093188 A093189 * A093191 A093192 A093193 KEYWORD nonn,tabl AUTHOR Ralf Stephan, Apr 20 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 23:46 EST 2022. Contains 358544 sequences. (Running on oeis4.)