# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a357459 Showing 1-1 of 1 %I A357459 #14 Sep 30 2022 03:51:00 %S A357459 0,1,1,3,4,7,10,17,22,34,46,66,88,123,160,218,283,375,482,630,799, %T A357459 1030,1299,1651,2066,2602,3230,4032,4976,6157,7554,9288,11326,13837, %U A357459 16793,20393,24632,29763,35783,43031,51527,61683,73577,87729,104252,123834,146664 %N A357459 The total number of fixed points among all partitions of n, when parts are written in nondecreasing order. %C A357459 For instance, the partition (1,3,3,3,5) = (y(1),y(2),y(3),y(4),y(5)) has 3 fixed points, since y(i) = i for i=1,3,5. %H A357459 A. Blecher and A. Knopfmacher, Fixed points and matching points in partitions, Ramanujan J. 58 (2022), 23-41. %F A357459 G.f.: (Product_{k>=1}(1/(1-q^k)))*Sum_{n>=1}q^(2*n-1)*Product_{k=n..2*n-2}(1-q^k). %e A357459 The 7 partitions of 5 are (1,1,1,1,1), (1,1,1,2), (1,2,2), (1,1,3), (1,4), (2,3), and (5), containing 1, 1, 2, 2, 1, 0, and 0 fixed points, respectively, and so a(5) = 1+1+2+2+1+0+0=7. %Y A357459 Cf. A001522 (parts decreasing), A099036. %K A357459 nonn %O A357459 0,4 %A A357459 _Jeremy Lovejoy_, Sep 29 2022 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE