A136311 Array read by antidiagonals: a(1) = 1; a(n+1) = a(n) + (largest k-gonal number <= a(n)).

1, 1, 2, 1, 2, 3, 1, 2, 3, 6, 1, 2, 3, 4, 12, 1, 2, 3, 4, 8, 22, 1, 2, 3, 4, 5, 12, 43, 1, 2, 3, 4, 5, 10, 21, 79, 1, 2, 3, 4, 5, 6, 15, 37, 157, 1, 2, 3, 4, 5, 6, 12, 27, 73, 310, 1, 2, 3, 4, 5, 6, 7, 18, 49, 137, 610, 1, 2, 3, 4, 5, 6, 7, 14, 33, 84, 258, 1205, 1, 2, 3, 4, 5, 6, 7, 8, 21, 61

Offset: 1

Author

Jonathan Vos Post, Mar 22 2008

Keywords

• easy
• nonn
• tabl

Examples

			The array begins:
==================================================================
n=..|.1.|.2.|.3.|.4.|..5.|..6.|..7.|..8.|...9.|..10.|..11.|...12.|
==================================================================
k=3.|.1.|.2.|.3.|.6.|.12.|.22.|.43.|.79.|.157.|.310.|.610.|.1205.|.A060985
k=4.|.1.|.2.|.3.|.4.|..8.|.12.|.21.|.37.|..73.|.137.|.258.|..514.|.A060984
k=5.|.1.|.2.|.3.|.4.|..5.|.10.|.15.|.27.|..49.|..84.|.154.|..299.|
k=6.|.1.|.2.|.3.|.4.|..5.|..6.|.12.|.18.|..33.|..61.|.106.|..197.|
k=7.|.1.|.2.|.3.|.4.|..5.|..6.|..7.|.14.|..21.|..39.|..73.|..128.|
k=8.|.1.|.2.|.3.|.4.|..5.|..6.|..7.|..8.|..16.|..24.|..45.|...85.|
k=9.|.1.|.2.|.3.|.4.|..5.|..6.|..7.|..8.|...9.|..18.|..27.|...51.|
==================================================================
		

Crossrefs

Cf. A060984, A060985.

Programs

Maple

A081422 := proc(k,n) n/2*((k-2)*n-k+4) ; end: A136311 := proc(k,n) option remember ; local aprev,n2 ; if n = 1 then RETURN(1) ; else aprev := A136311(k,n-1) ; for n2 from 0 do if A081422(k,n2) > aprev then RETURN( aprev+A081422(k,n2-1)); fi; od: fi ; end: for d from 4 to 20 do for n from 1 to d-3 do printf("%d,", A136311(d-n,n)) ; od: od: # R. J. Mathar, Jun 12 2008

Extensions

More terms from R. J. Mathar, Jun 12 2008