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 A210991 Total area of the shadows of the three views of the shell model of partitions with n regions. 6
 0, 3, 9, 18, 21, 35, 39, 58, 61, 67, 71, 99, 103, 110, 115, 152, 155, 161, 165, 175, 181, 186, 238, 242, 249, 254, 265, 269, 277, 283, 352, 355, 361, 365, 375, 381, 386, 401, 406, 415, 422, 428, 522, 526, 533, 538, 549, 553, 561, 567, 584, 590, 595, 606 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS It appears that if n is a partition number A000041 then the rotated structure with n regions shows each row as a partition of k such that A000041(k) = n (see example). For the definition of "regions of n" see A206437. LINKS Table of n, a(n) for n=0..53. FORMULA a(n) = A182181(n) + A182727(n) + A210692(n). a(A000041(n)) = 2*A006128(n) + A026905(n). EXAMPLE For n = 11 the three views of the shell model of partitions with 11 regions look like this: . . A182181(11) = 35 A210692(11) = 29 . . 1 1 . 1 1 . 1 1 . 1 1 . 1 1 1 1 . 1 1 1 1 . 1 1 1 1 1 1 . 2 1 1 1 1 2 . 2 1 1 1 1 1 1 2 . 3 2 2 2 1 1 1 1 2 2 3 . 6 3 4 2 5 3 4 2 3 2 1 1 2 3 4 5 6 . <------- Regions ------ ------------> N . L . a 1 . r * 2 . g * * 3 . e * 2 . s * * * 4 . t * * 3 . * * * * 5 . p * 2 . a * * * 4 . r * * 3 . t * * * * * 6 . s . . A182727(11) = 35 . The areas of the shadows of the three views are A182181(11) = 35, A182727(11) = 35 and A210692(11) = 29, therefore the total area of the three shadows is 35+35+29 = 99, so a(11) = 99. Since n = 11 is a partition number A000041 we can see that the rotated structure with 11 regions shows each row as a partition of 6 because A000041(6) = 11. See below: . . 6 . 3 3 . 4 2 . 2 2 2 . 5 1 . 3 2 1 . 4 1 1 . 2 2 1 1 . 3 1 1 1 . 2 1 1 1 1 . 1 1 1 1 1 1 . CROSSREFS Other versions: A207380, A210970, A210979, A210980, A210990. Cf. A000041, A026905, A135010, A138121, A141285, A182703, A194446, A182181, A182727, A186114, A206437, A210692. Sequence in context: A323199 A360365 A310332 * A112559 A030784 A203594 Adjacent sequences: A210988 A210989 A210990 * A210992 A210993 A210994 KEYWORD nonn AUTHOR Omar E. Pol, Apr 30 2012 STATUS approved

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Last modified June 8 18:04 EDT 2023. Contains 363165 sequences. (Running on oeis4.)