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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

Table of n, a(n) for n=1..56.

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)

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

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Last modified February 22 08:35 EST 2020. Contains 332133 sequences. (Running on oeis4.)