The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A182244 Sum of all parts of the shell model of partitions of A135010 with n regions. 9
 1, 4, 9, 11, 20, 23, 35, 37, 43, 46, 66, 69, 76, 80, 105, 107, 113, 116, 129, 134, 138, 176, 179, 186, 190, 204, 207, 216, 221, 270, 272, 278, 281, 294, 299, 303, 326, 330, 340, 346, 351, 420, 423, 430, 434, 448, 451, 460, 465, 492, 497, 501, 516, 523, 529, 616 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Omar E. Pol, Illustration of the seven regions of 5 FORMULA a(A000041(k)) = A066186(k), k >= 1. EXAMPLE The first four regions of the shell model of partitions are [1],[2, 1],[3, 1, 1],[2], so a(4) = (1)+(2+1)+(3+1+1)+(2) = 11. Written as a triangle begins: 1; 4; 9; 11,  20; 23,  35; 37,  43, 46, 66; 69,  76, 80,105; 107,113,116,129,134,138,176; 179,186,190,204,207,216,221,270; 272,278,281,294,299,303,326,330,340,346,351,420; 423,430,434,448,451,460,465,492,497,501,516,523,529,616; ... From Omar E. Pol, Aug 08 2013: (Start) Illustration of initial terms: .                                                _ _ _ _ _ .                                      _ _ _    |_ _ _    | .                            _ _ _ _  |_ _ _|_  |_ _ _|_  | .                    _ _    |_ _    | |_ _    | |_ _    | | .            _ _ _  |_ _|_  |_ _|_  | |_ _|_  | |_ _|_  | | .      _ _  |_ _  | |_ _  | |_ _  | | |_ _  | | |_ _  | | | .  _  |_  | |_  | | |_  | | |_  | | | |_  | | | |_  | | | | . |_| |_|_| |_|_|_| |_|_|_| |_|_|_|_| |_|_|_|_| |_|_|_|_|_| . .  1    4      9       11       20        23        35 . .                                          _ _ _ _ _ _ .                             _ _ _       |_ _ _      | .                _ _ _ _     |_ _ _|_     |_ _ _|_    | .   _ _         |_ _    |    |_ _    |    |_ _    |   | .  |_ _|_ _ _   |_ _|_ _|_   |_ _|_ _|_   |_ _|_ _|_  | .  |_ _ _    |  |_ _ _    |  |_ _ _    |  |_ _ _    | | .  |_ _ _|_  |  |_ _ _|_  |  |_ _ _|_  |  |_ _ _|_  | | .  |_ _    | |  |_ _    | |  |_ _    | |  |_ _    | | | .  |_ _|_  | |  |_ _|_  | |  |_ _|_  | |  |_ _|_  | | | .  |_ _  | | |  |_ _  | | |  |_ _  | | |  |_ _  | | | | .  |_  | | | |  |_  | | | |  |_  | | | |  |_  | | | | | .  |_|_|_|_|_|  |_|_|_|_|_|  |_|_|_|_|_|  |_|_|_|_|_|_| . .       37           43           46           66 (End) MATHEMATICA lex[n_]:=DeleteCases[Sort@PadRight[Reverse /@ IntegerPartitions@n], x_ /; x==0, 2]; A186412 = {}; l = {}; For[j = 1, j <= 56, j++,   mx = Max@lex[j][[j]]; AppendTo[l, mx];   For[i = j, i > 0, i--, If[l[[i]] > mx, Break[]]];   AppendTo[A186412, Total@Take[Reverse[First /@ lex[mx]], j - i]];   ]; Accumulate@A186412  (* Robert Price, Jul 25 2020 *) CROSSREFS Partial sums of A186412. Row j has length A187219(j). Right border gives A066186. Cf. A000041, A135010, A138121, A141285, A182244, A182181, A182276, A186114, A206437, A210990. Sequence in context: A329897 A312845 A312846 * A312847 A141365 A179055 Adjacent sequences:  A182241 A182242 A182243 * A182245 A182246 A182247 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Apr 23 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 18 11:20 EDT 2021. Contains 347518 sequences. (Running on oeis4.)