cp's OEIS Frontend

A077802 Sum of products of parts increased by 1 in hook partitions of n, where hook partitions are of the form h*1^(n-h).

%I A077802 #24 Feb 06 2022 12:58:19
%S A077802 1,2,7,18,41,88,183,374,757,1524,3059,6130,12273,24560,49135,98286,
%T A077802 196589,393196,786411,1572842,3145705,6291432,12582887,25165798,
%U A077802 50331621,100663268,201326563,402653154,805306337,1610612704
%N A077802 Sum of products of parts increased by 1 in hook partitions of n, where hook partitions are of the form h*1^(n-h).
%C A077802 It is not clear whether a(0) should be 1 or 0; this depends on whether the empty partition is a hook partition. By strict interpretation of the definition above, it is not; and except for n=0, there are exactly n hook partitions for each n. On the other hand, if defined as "a partition in whose Ferrers diagram every point is on the first row or column", the empty partition is a hook partition. - _Franklin T. Adams-Watters_, Jul 11 2009
%H A077802 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F A077802 From _Vladeta Jovovic_, Dec 05 2002: (Start)
%F A077802 a(n) = 3*2^n - n - 3, n > 0.
%F A077802 G.f.: x*(2-x)/(1-2*x)/(1-x)^2.
%F A077802 Recurrence: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). (End)
%F A077802 Row sums of triangle A132048. Equals binomial transform of [1, 1, 4, 2, 4, 2, 4, 2, 4, ...]. - _Gary W. Adamson_, Aug 08 2007
%F A077802 a(n) = A125128(n) + A000225(n), n >= 1. - _Miquel Cerda_, Aug 07 2016
%e A077802 The hook partitions of 4 are 4, 3+1, 2+1+1, 1+1+1+1; the corresponding products when parts are increased by 1 are 5, 8, 12, 16; and their sum is a(4) = 41.
%t A077802 s=0;lst={1};Do[s+=(s-n);AppendTo[lst, Abs[s]], {n, 2, 4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 10 2008 *)
%o A077802 (PARI) a(n)=if(n>0, 3*2^n - n - 3, 1) \\ _Charles R Greathouse IV_, Aug 08 2016
%Y A077802 Cf. A074141, A055010 (first differences), A042950 (second differences).
%Y A077802 Cf. A132048.
%Y A077802 Same as A095151 except for a(0). - _Franklin T. Adams-Watters_, Jul 11 2009
%K A077802 easy,nonn
%O A077802 0,2
%A A077802 _Alford Arnold_, Dec 02 2002
%E A077802 More terms from _John W. Layman_, Dec 05 2002