The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A126150 Symmetric triangle, read by rows of 2*n+1 terms, similar to triangle A008301. 5
 1, 1, 4, 1, 6, 24, 36, 24, 6, 96, 384, 636, 744, 636, 384, 96, 2976, 11904, 20256, 26304, 28536, 26304, 20256, 11904, 2976, 151416, 605664, 1042056, 1407024, 1650456, 1736064, 1650456, 1407024, 1042056, 605664, 151416, 11449296, 45797184 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA Sum_{k=0,2n} (-1)^k*C(2n,k)*T(n,k) = (-6)^n. EXAMPLE Triangle begins: 1; 1, 4, 1; 6, 24, 36, 24, 6; 96, 384, 636, 744, 636, 384, 96; 2976, 11904, 20256, 26304, 28536, 26304, 20256, 11904, 2976; 151416, 605664, 1042056, 1407024, 1650456, 1736064, 1650456, 1407024, 1042056, 605664, 151416; ... If we write the triangle like this: .......................... ....1; ................... ....1, ....4, ....1; ............ ....6, ...24, ...36, ...24, ....6; ..... ...96, ..384, ..636, ..744, ..636, ..384, ...96; .2976, 11904, 20256, 26304, 28536, 26304, 20256, 11904, .2976; then the first term in each row is the sum of the previous row: 2976 = 96 + 384 + 636 + 744 + 636 + 384 + 96 the next term is 4 times the first: 11904 = 4*2976, and the remaining terms in each row are obtained by the rule illustrated by: 20256 = 2*11904 - 2976 - 6*96; 26304 = 2*20256 - 11904 - 6*384; 28536 = 2*26304 - 20256 - 6*636; 26304 = 2*28536 - 26304 - 6*744; 20256 = 2*26304 - 28536 - 6*636; 11904 = 2*20256 - 26304 - 6*384; 2976 = 2*11904 - 20256 - 6*96. An alternate recurrence is illustrated by: 11904 = 2976 + 3*(96 + 384 + 636 + 744 + 636 + 384 + 96); 20256 = 11904 + 3*(384 + 636 + 744 + 636 + 384); 26304 = 20256 + 3*(636 + 744 + 636); 28536 = 26304 + 3*(744); and then for k>n, T(n,k) = T(n,2n-k). PROG (PARI) T(n, k)=local(p=3); if(2*n

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 April 17 16:12 EDT 2021. Contains 343063 sequences. (Running on oeis4.)