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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A276189 Triangle read by rows: T(n,k) = 2*(6*k^2 + 1)*(n + 1 - k) for 0 < k <= n; for k = 0, T(n,0) = n + 1. 2
 1, 2, 14, 3, 28, 50, 4, 42, 100, 110, 5, 56, 150, 220, 194, 6, 70, 200, 330, 388, 302, 7, 84, 250, 440, 582, 604, 434, 8, 98, 300, 550, 776, 906, 868, 590, 9, 112, 350, 660, 970, 1208, 1302, 1180, 770, 10, 126, 400, 770, 1164, 1510, 1736, 1770, 1540, 974, 11, 140, 450, 880, 1358, 1812, 2170, 2360, 2310, 1948, 1202 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The row sums of the triangle provide the positive terms of A000583. Similar triangles can be generated by the formula P(n,k,m) = (Q(k+1,m)-Q(k,m))*(n+1-k), where Q(i,r) = i^r-(i-1)^r, 0 < k <= n, and P(n,0,m) = n+1. T(n,k) is the case m=4, that is T(n,k) = P(n,k,4). LINKS Michael De Vlieger, Table of n, a(n) for n = 0..11475 (rows 0 <= n <= 150, flattened) FORMULA T(n,n-h) = (h+1)*A005914(n-h) for 0 <= h <= n. Therefore, the main diagonal of the triangle is A005914. Sum_{k=0..n} T(n,k) = T(n,0)^4 = A000583(n+1). EXAMPLE Triangle starts: ---------------------------------------------- n \ k | 0 1 2 3 4 5 6 7 ---------------------------------------------- 0 | 1; 1 | 2, 14; 2 | 3, 28, 50; 3 | 4, 42, 100, 110; 4 | 5, 56, 150, 220, 194; 5 | 6, 70, 200, 330, 388, 302; 6 | 7, 84, 250, 440, 582, 604, 434; 7 | 8, 98, 300, 550, 776, 906, 868, 590; ... MATHEMATICA Table[If[k == 0, n + 1, 2 (6 k^2 + 1) (n + 1 - k)], {n, 0, 9}, {k, 0, n}] // Flatten (* Michael De Vlieger, Aug 29 2016 *) PROG (Magma) [IsZero(k) select n+1 else 2*(6*k^2+1)*(n+1-k): k in [0..n], n in [0..10]]; (Magma) /* As triangle (see the second comment): */ m:=4; Q:=func; P:=func; [[P(n, k, m): k in [0..n]]: n in [0..10]]; CROSSREFS Cf. A000583, A005914, A276158. Sequence in context: A298800 A138907 A336837 * A281944 A306724 A316909 Adjacent sequences: A276186 A276187 A276188 * A276190 A276191 A276192 KEYWORD nonn,tabl AUTHOR Stefano Maruelli, Aug 24 2016 EXTENSIONS Corrected, rewritten and extended by Bruno Berselli, Aug 31 2016 a(40) ff. corrected by Georg Fischer, Nov 08 2021 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 April 19 11:14 EDT 2024. Contains 371791 sequences. (Running on oeis4.)