A111712 Arithmetic mean of the n-th row of triangle mentioned in A111710.

1, 3, 6, 10, 16, 22, 31, 39, 51, 61, 76, 88, 106, 120, 141, 157, 181, 199, 226, 246, 276, 298, 331, 355, 391, 417, 456, 484, 526, 556, 601, 633, 681, 715, 766, 802, 856, 894, 951, 991, 1051, 1093, 1156, 1200, 1266, 1312, 1381, 1429, 1501, 1551, 1626, 1678

Offset: 1

Author

Amarnath Murthy, Aug 24 2005

Keywords

• easy
• nonn

Examples

			a(4) = (8+9+10+13)/4 =10
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A111710, A111711.

Partial sums of A195013 prepended with 1.

Programs

Haskell

a111712 n = a111712_list !! (n-1)
a111712_list = scanl (+) 1 a195013_list
-- Reinhard Zumkeller, Apr 06 2015

Mathematica

With[{r = Range[50]}, Accumulate[Join[{1}, Riffle[2*r, 3*r]]]] (* or *)
LinearRecurrence[{1, 2, -2, -1, 1}, {1, 3, 6, 10, 16}, 100] (* Paolo Xausa, Feb 09 2024 *)

Formula

a(1)=1, a(2n) = a(2n-1)+2n, a(2n+1)=a(2n)+3n. a(n) = A111711(n)+floor(n/2). - Franklin T. Adams-Watters, May 01 2006

Extensions

More terms from Franklin T. Adams-Watters, May 01 2006