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

1,2

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).

Formula

a(1)=1, a(2n) = a(2n-1)+2n, a(2n+1)=a(2n)+3n. a(n) = A117111(n)+floor(n/2). - Franklin T. Adams-Watters, May 01 2006

Example

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

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 *)

Prog

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

Crossrefs

Cf. A111710, A111711.

Partial sums of A195013 prepended with 1.

Sequence in context: A283503 A294481 A049697 * A293407 A194144 A330133

Adjacent sequences: A111709 A111710 A111711 * A111713 A111714 A111715

Keyword

easy,nonn

Author

Amarnath Murthy, Aug 24 2005

Extensions

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

Status

approved