cp's OEIS Frontend

A162934 Shift sequence A162932 twice then subtract from the original sequence.

%I A162934 #13 Dec 08 2024 10:20:50
%S A162934 1,0,0,1,0,0,2,0,0,3,1,0,4,2,2,5,3,4,9,5,6,13,11,10,19,17,19,28,27,31,
%T A162934 44,41,49,66,68,74,98,104,118,145,157,178,220,234,268,322,354,397,473,
%U A162934 521,591,686,765,863,1003,1107,1254,1444,1609
%N A162934 Shift sequence A162932 twice then subtract from the original sequence.
%C A162934 From _Alford Arnold_, Dec 17 2009: (Start)
%C A162934 At n = 24, six of the partitions can be associated with the sixth row of this triangular array:
%C A162934  333
%C A162934  444 3333
%C A162934  555 4443 33333
%C A162934  666 5553 44433 333333
%C A162934  777 6663 55533 444333 3333333
%C A162934  888 7773 66633 555333 4443333 33333333
%C A162934 The other three partitions are new; and hence on their first row, so 6*1 + 1*3 = 9.
%C A162934 In a similar manner, the 44 cases at n = 36 can be computed using the array row numbers and the number of applicable partitions. Thus we have:
%C A162934 (10, 5, 3, 2, 1) times (1, 3, 2, 3, 7) providing 10 + 15 + 6 + 6 + 7 = 44 cases. (End)
%F A162934 G.f.: Sum_{n >= 0} q^(3*n+6)/Product_{k = 1..n} 1 - q^(k+2). - _Peter Bala_, Dec 01 2024
%e A162934 For n = 24, the sequence counts these nine partitions of 24: 888, 7773, 66633, 55554, 555333, 4443333, 6666, 444444, 33333333.
%Y A162934 Cf. A000041, A002865, A053445, A162932.
%K A162934 nonn,easy
%O A162934 6,7
%A A162934 _Alford Arnold_, Aug 05 2009, Aug 06 2009
%E A162934 More terms from _Alford Arnold_, Dec 17 2009
%E A162934 More terms from _Joerg Arndt_, Jul 16 2015