The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons 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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A113582 Triangle T(n,m) read by rows: T(n,m) = (n - m)*(n - m + 1)*m*(m + 1)/4 + 1. 4
 1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 7, 10, 7, 1, 1, 11, 19, 19, 11, 1, 1, 16, 31, 37, 31, 16, 1, 1, 22, 46, 61, 61, 46, 22, 1, 1, 29, 64, 91, 101, 91, 64, 29, 1, 1, 37, 85, 127, 151, 151, 127, 85, 37, 1, 1, 46, 109, 169, 211, 226, 211, 169, 109, 46, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS From Paul Barry, Jan 07 2009: (Start) This triangle follows a general construction method as follows: Let a(n) be an integer sequence with a(0)=1, a(1)=1. Then T(n,k,r) := [k<=n](1+r*a(k)*a(n-k)) defines a symmetrical triangle. Row sums are n + 1 + r*Sum_{k=0..n} a(k)*a(n-k) and central coefficients are 1+r*a(n)^2. Here a(n) = C(n+1,2) and r=1. Row sums are A154322 and central coefficients are A154323. (End) LINKS G. C. Greubel, Rows n=0..100 of triangle, flattened FORMULA T(n,m) = (n - m)*(n - m + 1)*m*(m + 1)/4 + 1. EXAMPLE {1}, {1, 1}, {1, 2, 1}, {1, 4, 4, 1}, {1, 7, 10, 7, 1}, {1, 11, 19, 19, 11, 1}, {1, 16, 31, 37, 31, 16, 1}, {1, 22, 46, 61, 61, 46, 22, 1}, {1, 29, 64, 91, 101, 91, 64, 29, 1}, {1, 37, 85, 127, 151, 151, 127, 85, 37, 1}, {1, 46, 109, 169, 211, 226, 211, 169, 109, 46, 1} MATHEMATICA t[n_, m_] = (n - m)*(n - m + 1)*m*(m + 1)/4 + 1; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]//Flatten PROG (MAGMA) /* As triangle: */ [[(n-m)*(n-m+1)*m*(m+1)/4+1: m in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Sep 12 2016 (PARI) for(n=0, 15, for(k=0, n, print1((n-k)*(n-k+1)*k*(k+1)/4 + 1, ", "))) \\ G. C. Greubel, Aug 31 2018 CROSSREFS Sequence in context: A128562 A034368 A296157 * A347147 A295213 A118245 Adjacent sequences:  A113579 A113580 A113581 * A113583 A113584 A113585 KEYWORD nonn,tabl,easy AUTHOR Roger L. Bagula, Aug 25 2008 STATUS approved

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

Last modified December 7 19:20 EST 2021. Contains 349585 sequences. (Running on oeis4.)